Estimation of the Equivalent Number of Looks in SAR Images Based on Singular Value Decomposition

In this letter, a singular value decomposition (SVD)-based method for estimating the equivalent number of looks (ENL) in synthetic aperture radar (SAR) images is proposed. First, SAR images are logarithmically scaled to change the multiplicative speckle into additive noise. Assuming that the multiplicative speckle is a gamma random variable with unit mean, a monotone function is established between the ENL and the variance of the additive noise, thus transforming the ENL estimation problem into estimating the variance of the additive noise. Then SVD is applied to the logarithmic image in a window with certain size to obtain its singular values. By making use of an empirical linear relationship between the average of the smallest singular values and the standard deviation of the noise in the logarithmic image, the variance of the additive noise is finally estimated. Experiments of both simulated and real SAR images demonstrated the effectiveness of the proposed method.